It was the first league defeat for Arsene Wenger's men since they lost to Liverpool on the opening day of the season and their first on the road since March.
Ashley Williams powered home a towering header in the 86th minute as Everton fought back to claim a 2-1 win over Arsenal as the title hopefuls blew the chance to return to the English Premier League summit on Tuesday.
It was the first league defeat for Arsene Wenger's men since they lost to Liverpool on the opening day of the season and their first on the road since March.
More importantly, it handed Chelsea the chance to go six points clear at the top when they visit bottom club Sunderland on Wednesday.
It looked like business as usual for the visitors, who have been scoring freely in recent weeks, when Alexis Sanchez netted his 12th league goal of the season with a deflected free kick after 20 minutes.
Everton though warmed to the task, levelling through Seamus Coleman's header a minute before halftime.
With the seconds ticking away towards the end, Williams rose high to nod Ross Barkley's corner into the net for his first Everton goal, securing the team's first win since the end of October.
It moved Everton up to seventh in the table and offered some cheer to manager Ronald Koeman.
"We showed unbelievable spirit to come back and we deserved the win," the Dutchman told BT Sport.
Everton struggled for confidence in the early stages as they retreated, inviting Arsenal to attack.
Francis Coquelin was brought down on the edge of the area and Sanchez stepped up to hit a tame free kick that looked to be covered by Maarten Stekelenburg until it deflected off Williams and beat the keeper's outstretched hand.
The goal put Sanchez joint top of the league's scoring charts with Chelsea's Diego Costa.
It also seemed to spark life into the hosts who gradually came out of their shells with Aaron Lennon slicing an effort wide before Coleman levelled with a glancing header from Leighton Baines' cross.
Mesut Ozil blasted a good chance over for Arsenal at the start of the second half but Everton were on top and pushing for the winner when Williams sent Goodison Park wild.
In a frenetic finale, Everton defender Phil Jagielka was sent off for a second booking in the fourth minute of stoppage time.
Arsenal also had two efforts cleared off the line and somehow prevented the home team grabbing a third goal when keeper Petr Cech was caught upfield.
Bournemouth send Leicester back into doldrums
English champions Leicester City failed to continue their mini-revival after a clinical finish by Bournemouth's Marc Pugh condemned them to a 1-0 away defeat in a scrappy Premier League clash.
The outcome kept 14th-placed Leicester close to the relegation zone on 16 points, four above the bottom three who play their games in hand on Wednesday, and was a setback after Saturday's 4-2 home win over fourth-placed Manchester City.
Bournemouth, who kept the visitors on the back foot for much of the contest, grabbed a 34th-minute winner when Pugh swept in a rebound from 13 metres after Leicester keeper Ron-Robert Zieler did well to parry a close range shot by Benik Afobe.
Leicester had missed an early chance in the seventh minute when striker Jamie Vardy, who scored a hat-trick against City, rounded keeper Artur Boruc with a heavy first touch and saw his harmless shot from a tight angle blocked by a defender.
Boruc came to the hosts' rescue in the 90th minute when he blocked a close-range shot by substitute Leonardo Ulloa to help seal the points as Bournemouth moved up to eighth on 21 points.
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